Activity – 1
Is it interesting to see this pattern ?
Verify it. Can you frame 4 such new surds?
Activity – 2
Take a graph sheet and mark O, A, B, C as follows.
In the square OABC,
OA = AB = BC = OC = 1unit
Consider right angled DOAC
AC = √[12 +12]
= √2 unit [By Pythagoras theorem]
The length of the diagonal (hypotenuse)
AC = √2 , which is a surd.
Consider the following graphs:
Let us try to find the length of AC in two different ways :
AC = AD +DE +EC
(diagonals of units squares)
AC = 3√2 units
AC = √[OA2 +OC2] = √[32 +32]
= √[9 + 9 ]
AC = √18 units
Are they equal? Discuss. Can you verify the same by taking different squares of different lengths?
Activity − 3
The following list shows the mean distance of the planets of the solar system from the Sun. Complete the following table. Then arrange in order of magnitude starting with the distance of the planet closest to the Sun.